Modeling Variables with a Detection Limit using a Truncated Normal Distribution with Censoring

TL;DR

This paper introduces tcensReg, a regression method for censored data with detection limits and domain restrictions, based on a truncated normal distribution, outperforming existing methods in bias and MSE.

Contribution

The paper presents a novel maximum likelihood estimation approach for censored, domain-restricted data using a truncated normal model, improving accuracy over traditional methods.

Findings

tcensReg reduces bias and MSE compared to Tobit and imputation methods.

Simulation studies demonstrate superior performance of tcensReg.

Application to ophthalmology data illustrates practical utility.

Abstract

When data are collected subject to a detection limit, observations below the detection limit may be considered censored. In addition, the domain of such observations may be restricted; for example, values may be required to be non-negative. We propose a regression method for censored observations that also accounts for domain restriction. The method finds maximum likelihood estimates assuming an underlying truncated normal distribution. We show that our method, tcensReg, outperforms other methods commonly used for data with detection limits such as Tobit regression and single imputation of the detection limit or half detection limit with respect to bias and mean squared error under a range of simulation settings. We apply our method to analyze vision quality data collected from ophthalmology clinical trials comparing different types of intraocular lenses implanted during cataract surgery.